What is the area of the figure?
What is the area of the figure?

Answer:

Are there any options for an answer?

Step-by-step explanation:

Parameterize the line segment (call it [tex]C[/tex]) by

[tex]\vec r(t)=(1-t)(4,4,2)+t(5,8,-4)=(4+t,4+4t,2-6t)[/tex]

with [tex]0\le t\le1[/tex]. Then the line integral of [tex]\vec f(x,y)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k[/tex] is

[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(4+4t,4+t,3)\cdot(1,4,-6)\,\mathrm dt=\int_0^1(2+8t)\,\mathrm dt=6[/tex]

Final answer:

To evaluate the line integral of the given vector field along the line segment, parametric equations are established, and the integral is simplified to a single-variable integral, resulting in a value of 12.

Explanation:

To evaluate the line integral of f=yi+xj+3k along the segment from (4,4,2) to (5,8,-4), first we find parametric equations for the line segment. The parametric equations are x=4+t, y=4+4t, z=2-6t, where t varies from 0 to 1. We then express the vector field in terms of t, yielding f(t) = (4+4t)i + (4+t)j + 3k. The derivative of the vector position is dr/dt = i + 4j - 6k. The line integral becomes an integral with respect to t, from 0 to 1, of the dot product of f(t) and dr/dt, which simplifies to ∫(8 + 52t - 18)dt = ∫(44t - 10)dt.

Integrating from 0 to 1 gives the final answer as 22 - 10 = 12. This approach demonstrates how converting a line integral into a single-variable integral simplifies the calculation.

Answer: First Option

The number of multiples of 9 is 211

Step-by-step explanation:

Note that the first multiplo of 9 between 100 and 2000 is number 108. The last multiple of 9 is 1998.

If we use the arithmetic sequence to perform the calculation

[tex]a_n = a_1 + d(n - 1)[/tex]

So the first term [tex]a_1[/tex] is:

[tex]a_1 = 108[/tex]

The last term [tex]a_n[/tex] is

[tex]a_n = 1998[/tex]

The common difference is

[tex]d = 9[/tex]

Thus

[tex]1998 = 108 + 9(n-1)[/tex]

We solve the equation for n and obtain the number of multiples of 9.

[tex]1998-108 = 9(n-1)\\\\\frac{1998-108}{9}=n-1\\\\n = 210 +1\\\\n = 211[/tex]

196.00000000000000000000000

You need 3a^3 to equal a^3, so you would need at subtract 2a^3.

Since the problem is addition, add - 2a^3:

3a^3 + -2a^3 = 3a^3 - 2a^3 = a^3

Then you have -5b^3 and you need it to equal b^^3, so you would need to add 6b^3:

-5b^3 + 6b^3 = b^3

First box would be -2

Second box would be 6

200-1500 dollars I believe

Answer:

15/20 or 3/4

Step-by-step explanation:

9 green marbles(GM) + 5 yellow marbles(YM) + 6 red marbles(RM) = 20 marbles total(TM)

GM = 9/20

YM = 5/20

RM = 6/20

TM = 20/20

For the probability of choosing a GM or RM you just add their respective values:

9/20 + 6/20 = 15/20

Simplified this answer is 3/4

Probability of selecting a green or red marble is 3/4

Given that;

Number of green marble = 9

Number of red marble = 6

Number of yellow marble = 5

Find:

Probability of selecting a green or red marble

Computation:

Probability of selecting a green = 9 / [9 + 6 + 5]

Probability of selecting a green = 9 / 20

Probability of selecting a red = 6 / [9 + 6 + 5]

Probability of selecting a green = 6 / 20

Probability of selecting a green or red marble = [9/20] + [6/20]

Probability of selecting a green or red marble = 15 / 20

Probability of selecting a green or red marble = 3/4

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Answer:

Critical points of an equation are the zeroes of its first derivative. Since you have already provided me with the derivative (thanks for saving me the effort :) ), I am just going to start the process.

tan (x) + x(sec^2(x)) = 0

Solving this equation (using a graphing calculator set to radians), it is only true when x = 0.

So, 0 is a critical point of this function.

Hope this helped!

The derivative of tan(x) is sec^2(x) and the critical points for xtanx occur at x = π/2 + nπ.

Derivative of tan(x) can be found by using the formula: d/dx(tan(x)) = sec^2(x). Critical points for xtanx can be obtained by setting the derivative equal to zero and solving for x. In this case, the critical points are where sec^2(x) = 0, which occurs when x = π/2 + nπ, where n is an integer.

Answer:

A

Step-by-step explanation:

x² + 10x + 24 = 0

Here, a = 1, b = 10, c = 24.  Factoring using the AC method:

ac = 1×24 = 24

Factors of 24 that add up to 10 are +4 and +6.

Therefore:

(x + 4) (x + 6) = 0

x + 4 = 0, x + 6 = 0

x = -4, x = -6

The roots are -4 and -6.  Added together:

-4 + -6 = -10

Answer A.

The required sum of the roots of the quadratic equation x² + 10x + 24 = 0 is -10.

In mathematics, the roots of an equation are the values of the variable that satisfy the equation.

Here,
To find the roots of the quadratic equation x² + 10x + 24 = 0, we can use the quadratic formula,

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 10, and c = 24. Substituting these values, we get:

x = (-10 ± √(10² - 4(1)(24))) / (2(1))

x = (-10 ± √4) / 2

x = -5 ± 1

Therefore, the roots of the quadratic equation are x = -4 and x = -6.

The sum of these roots is -4 + (-6) = -10

Therefore, the sum of the roots of the quadratic equation x² + 10x + 24 = 0 is -10.

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Diagonal of base is 8.94(approx)

If you need an explanation please contact me.

I apologize if this is not what you meant.

Answer:

The available credit is [tex]\$ 2,749[/tex]

Step-by-step explanation:

we know that

The available credit is equal to the credit limit minus the purchases

so

[tex]4,000-(425.36+358.33+377.11+90.20)=\$ 2,749[/tex]

Answer: Option C. Ellipse

Step-by-step explanation:

The general equation of an ellipse has the following form:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1[/tex]

Where the point (h, k) is the center of the ellipse

In this case we have the equation

[tex]\frac{(x-9)^2}{4} + \frac{(y+2)^2}{25} =1[/tex]

Note that its shape matches that of a ellipse with center (9, -2)

[tex]a=\sqrt{4} \\a=2\\\\\\b=\sqrt{25}\\b=5[/tex]

Therefore the answer is the obtion C

Answer:

C

Step-by-step explanation:

Answer:

The graph c.

Step-by-step explanation:

We know from the function f(x) = 5sin(-2t) three things:

1. The amplitude is 5.

2. The period is π.

3. Because of the negative in the argumen, the graph will be reflected over the y-axis (Compared to the graph of sin(x))

Then, evaluating all the functions we find:

1. All of graphs have an amplitude of 5.

2. The graph b has a period of 2π.

3. The graph a is not reflected over the y-axis.

Then, the correct graph is the graph letter C.

The Graph of the function f(t) = 5 sin(-2t) is graph (b) in the image you provided.

This can be seen by noting that the function f(t) = 5 sin(-2t) is a sine function with a period of π, amplitude of 5, and horizontal shift of π/2 to the right. Graph (b) in the image matches these characteristics.

Amplitude: The amplitude of the function is 5, which is the absolute value of the coefficient in front of the sine term.

Period: The period of the function is π/2, which is the reciprocal of the absolute value of the coefficient multiplying the t term.

Phase shift: The function has a phase shift of π, which means that the graph is shifted to the left by π units.

The graph on the left has all of these features:

It has an amplitude of 5.

It has a period of π/2.

It is shifted to the left by π units.

The other graphs in the image do not match these characteristics:

Graph (a) has a period of 2π, not π.

Graph (c) has an amplitude of 1, not 5.

Graph (d) has a horizontal shift of −π/2, not π/2.

Therefore, the correct graph is graph (b).

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Answer:

any list of numbers, an arrangement of quantities whose positions are based upon the natural numbers.

Step-by-step explanation:

Answer with explanation:

A Series is:

⇒a summation of quantities whose positions are based upon the natural numbers

This can be explained in the following way

Consider , the arrangement of Quantities

a,   a a,   a a a,   a a a a,  a a a a a,  a a a a a a, a a a a a a a, a a a a a a a a,..........

1  ,    1+1=2  , 1+1+1=3 ,   1+1+1+1= 4     ,       1+1+1+1+1=5  ,      1+1+1+1+1+1=6  ,                1+1+1+1+1+1+1=7    ,    1+1+1+1+1+1+1+1=8

Here, Alphabet "a" are Quantity.

⇒1,2,3,.....are position of Quantity  represented by Natural Number.

In terms of Summation , it can be written as:

 1+2+3+4+5+6+7+8.............

[tex]=\sum_{k=1}^{n} k[/tex]

Answer:

  all integers where n ≥ 1

Step-by-step explanation:

n is a counting number, since it counts the terms of the sequence. It is in the set {1, 2, 3, ...}, any of the integers 1 or greater.

Answer:

The third one

Step-by-step explanation:

Slope is rise/run

This graphs shows the line going up by 2 and to the right 3

The graph that has a slope equal to 2/3 is Option(C) .

Slope of a straight line is defined as the inclination of the line with respect to the coordinate axis. The slope is also measure of the tangent of angle with which the line is inclined to the axis.

Slope of a straight line can be found using two given points say (x1,y1) and (x2,y2).

Slope (m) = (y2 - y1) / (x2 - x1) .

We check the graph at Option(C).

The coordinate of the point where the graph has 2 units distance with the y-axis is (4.5,2) and the coordinate of the point where the graph has 3 units distance with the x-axis is (1.5,0).

We have y2 = 2 , y1 = 0, x1 = 4.5, x2 = 1.5 .

Thus slope = (y2  y2)/(x2 - x1) = (2 - 0)/(4.5 - 1.5) = 2/3

Therefore, the graph that has a slope equal to 2/3 is the graph in  Option(C) .

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A. a number and three is at most two

The inequality states that a number and three is less than or equal to two.

“Less than or equal to” means the same thing as “at most”.

So, the inequality states that a number and three is at most two.

ANSWER

A number and three is at most two.

EXPLANATION

The given inequality is

[tex]x + 3 \leqslant 2[/tex]

The emphasis is on the inequality sign.

The inequality sign is "≤"

"≤" means less or equal to.

"≤" also means at most

Therefore,

[tex]x + 3 \leqslant 2[/tex]

means the sum of a number and 3 is at most 2.

The correct choice is A

Answer:

Option Z

The graph in the attached figure

Step-by-step explanation:

Let

x----> the number of chickens sandwiches

y----> the number of hamburgers

we know that

[tex]x+y\leq 40[/tex] ----> inequality A

[tex]4x+2y\geq 100[/tex] ----> inequality B

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Answer:

D. This should be the correct answer as it shows similarity through AAA.

A. is not correct because one side is not enough to determine similarity.

B. is not correct because it angle Z & angle Y are not similar.

C is not correct because line ZY and YX are not similar.

Answer:

the common ratio is 6

Step-by-step explanation:

because 4 times 6 is 24

24 times 6 is 144

144 times 6 is 864

Answer:

6.

Step-by-step explanation:

The common ratio is the value with which we multiply each term to get the next term.

Common ratio = 24/4 = 144/24 = 864 / 144

= 6 (answer).

Answer:

a. Managing Income

Step-by-step explanation:

Justin and his wife should pay more attention to managing liquidity (option B). This means they need to better manage their income, savings, and expenses to be able to save more money. Their current spending seems to be higher than their income which is not sustainable in the long term.

Based on the information provided, option B, managing liquidity, is the area that Justin and his wife should focus on for their financial planning. Liquidity refers to the ability to cover immediate expenses or debts. Given they typically spend $3,000 per month and their combined income seems less than their outflow, it suggests that they might be having challenges saving money. Therefore, focusing on managing liquidity could help them better track their cash flow and enhance their savings plan.

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Answer:

it's a geometric sequence. the explicit formula is: 8 times 1/2^n-1

Answer:

B. Geometric. [tex]f(n) =16\cdot \left(\frac{1}{2}\right)^{n}[/tex], [tex]\forall n \in \mathbb{N}_{O}[/tex]

Step-by-step explanation:

The problems shows a geometric sequence, since the statement describes succesive halves that are consumed by Achilles. The formula is:

[tex]f(n) =\Sigma_{i=1}^{n} 16\cdot \left(\frac{1}{2}\right)^{i}[/tex], [tex]\forall n \in \mathbb{N}[/tex]

Answer: last option.

Step-by-step explanation:

We know that the line is vertical and it passes through the point (3, -3).

Then, since it is vertical, the equation of this line will have the following form:

[tex]x = a[/tex]

Where "a" is the value of the x-coordinate (Because vertical lines passes through all points with the same x-coordinate)

Then, you can observe in the given point that the x-coordinate is 3. Therefore, the equation of the line is:

[tex]x=3[/tex]

ANSWER

[tex]x = 3[/tex]

EXPLANATION

The equation of a vertical line that passes through

[tex](x_1,y_1)[/tex]

is given by

[tex]x = x_1[/tex]

That is x equals the x-value of the point.

Since the vertical line passes through (3,-3).

Therefore the equation of a vertical line that passes through the point (3, –3).

[tex]x = 3[/tex]

Answer:

125 miles

Step-by-step explanation:

Write formulas for the amount of $ that would be due each of the two companies and set these equal to one another prior to solving for the number of days:

A:  $35 + ($0.45/mile)x  

B:  $60 + ($0.25/mile)x

Then $35 + ($0.45/mile)x = $60 + ($0.25/mile)x, or

($0.20/mile)x = $25

                                                                       $25

dividing both sides by $0.20 yields  x = ------------------- = 125 miles

                                                                    $0.20/mile

The charges made by the two companies would become equal after the 125th mile.  After that, Company B would become cheaper.

Ms. Call would need to drive at least 125 miles for the rental from Company B to be more cost-effective.

To find out when Company B becomes a better deal, we need to set up an equality and solve it for the number of miles. We can create the equation as follows:

Company A cost = Company B cost.

So, $35 + $0.45x = $60 + $0.25x.

Here x represents the number of miles driven. If we simplify this equation, we have:

$0.20x = $25.

Thus, solving for x: x = 25/0.20 = 125

So, Ms. Call would need to drive at least 125 miles in order for Company B to be a better deal.

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Answer: 0) 0.22

              1) 0.20

              2) 0.12

              3) 0.14

              4) 0.28

              5) 0.04

Step-by-step explanation:

The total frequency is 33+30+18+21+42+6 = 150.  This means they ran the experiment 150 times.  The probability (P) is calculated by the satisfactory number of outcomes (frequency) divided by the total number of experiments/outcomes (total frequency):

[tex]\begin{array}{c|c||lc}\underline{x}&\underline{f}&\underline{f\div 150}&\underline{\text{P}}\\0&33&33\div 150=&0.22\\1&30&30\div150=&0.20\\2&18&18\div 150=&0.12\\3&21&21\div 150=&0.14\\4&42&42\div 150=&0.28\\5&6&6\div 150=&0.04\end{array}\right][/tex]

Answer:

20kph

Step-by-step explanation:

10 * 2 = 20

ANSWER

d. The amplitude is 2

period:

[tex]\frac{2\pi}{3} [/tex]

EXPLANATION

The given function is

[tex]f(t) = - 2 \cos(3t) [/tex]

This function is of the form,

f(t) = a cos(bt)

The amplitude of this function is |a|

where a=-2

[tex] | - 2| = 2[/tex]

The period of this function is given by,

[tex]T= \frac{2\pi}{b} [/tex]

But b=3,

[tex]T= \frac{2\pi}{3} [/tex]

Option D is correct.

Answer:

It would be 6 right?

Step-by-step explanation:

The reason is because parallelograms have 2 pairs of parallel sides. So in this case, JK=LM and JM=KL.

Answer:

The range is 1

Step-by-step explanation:

To calculate range, you subtract the lowest value from the highest value.

The lowest is 5 here and the highest is 6. The range is 6-5 which equals 1.

Answer:

1

Step-by-step explanation:

You are finding the range, which can be found by subtracting the smallest number from the greatest number.

Smallest number = 5, Greatest number = 6

6 - 5 = 1

1 is your range answer.

~

Answer: Last Option

[tex]Y =\frac{1}{2}cosx + 3[/tex]

Step-by-step explanation:

If the graph of the function [tex]y=kf(x) +d[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <k <1[/tex] then the graph is compressed vertically by a factor k.

If  [tex]|k| > 1[/tex] then the graph is stretched vertically by a factor k

If [tex]k <0[/tex]  then the graph is reflected on the x axis.

If [tex]d> 0[/tex] the graph moves vertically upwards d units.

If [tex]d <0[/tex] the graph moves vertically down  d units.

In this problem we have the function [tex]y = cos⁡x[/tex]

And we know that The graph of [tex]y = cos⁡x[/tex] is transformed with  a vertical compression by a factor of 1/2 and a translation 3 units up

therefore it is true that [tex]0 <k <1[/tex] and [tex]k=\frac{1}{2}[/tex] and  [tex]d =3> 0[/tex]

Therefore the  new equation is:

[tex]Y =\frac{1}{2}cosx + 3[/tex]

The upper value of the confidence interval is 0.478.

A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.

Given:

A random sample of 150 people from Iowa has been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200. Construct a 95% confidence interval for the population proportion of people in Iowa with cholesterol levels over 200.

p' = 60/150

p' = 0.4

n = 150

95% Â → z(1-a/2) = 1.96

So the interval is:

[0.4 - 1.96{sqrt(0.4(0.6)/150)}], 0.4 + 1.96{sqrt(0.4(0.6)/150)}

= (0.322, 0.478)

Therefore, the interval is (0.322, 0.478).

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Using the confidence interval formula for a proportion, we find that the upper limit is approximately 0.468, indicating a maximum of 46.8% of the population might have cholesterol levels above 200 with 95% confidence.

First, calculate the sample proportion (p) by dividing the number of positive outcomes (60) by the total sample size (150), which gives us p = 0.4. The formula for the confidence interval of a proportion is given by p ± Z*√(p(1-p)/n), where Z is the Z-score corresponding to the confidence level (for 95%, Z = 1.96), p is the sample proportion, and n is the sample size. Plugging in the values, we calculate:

Lower limit = 0.4 - 1.96*√(0.4*0.6/150) ≈ 0.332

Upper limit = 0.4 + 1.96*√(0.4*0.6/150) ≈ 0.468

The upper value of the confidence interval is approximately 0.468, which means we are 95% confident that the true proportion of people in Iowa with cholesterol levels over 200 is less than 46.8%.